New Foundations Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  NFE Home  >  Th. List  >  rexeqbii Unicode version

Theorem rexeqbii 2645
 Description: Equality deduction for restricted existential quantifier, changing both formula and quantifier domain. Inference form. (Contributed by David Moews, 1-May-2017.)
Hypotheses
Ref Expression
raleqbii.1
raleqbii.2
Assertion
Ref Expression
rexeqbii

Proof of Theorem rexeqbii
StepHypRef Expression
1 raleqbii.1 . . . 4
21eleq2i 2417 . . 3
3 raleqbii.2 . . 3
42, 3anbi12i 678 . 2
54rexbii2 2643 1
 Colors of variables: wff setvar class Syntax hints:   wb 176   wceq 1642   wcel 1710  wrex 2615 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-11 1746  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542  df-cleq 2346  df-clel 2349  df-rex 2620 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator